Survival and Perception Checks / Magical Tracking
While you can't call for what check to make, you can describe what you'd like to do. Tracking is something that any character is capable of through Survival and possibly Perception(PHB, 178).
Survival. The DM might ask you to make a Wisdom (Survival) check to follow tracks, hunt wild game, guide your group through frozen wastelands, identify signs that owlbears live nearby, predict the weather, or avoid quicksand and other natural hazards.
In the future, you can also utilize Hunter's Mark to get a better chance of finding them.
you have advantage on any Wisdom (Perception) or Wisdom (Survival) check you make to find it
Using Magic, if available
There are a few options available to you, should you have anyone with access and spell slots available:
- Locate Object - 2nd Level Spell, 1 Action
- Locate Creature - 4th Level Spell, 1 Action
Locate Object is probably your best bet as the spell cost is smaller than Locate Creature - but either should work.
Scrying is interesting, but the 10 minutes it takes to cast it would hurt more than help.
Distance to the Rogue
Assuming the Rogue has a 15 second head start (as stated), that's 2.5 rounds. If they Hid in the first round, then they could do a single move that round, a double the next and maybe give them another single move for the .5 round (but that's being very generous and assuming your party was still fighting during that round.) If we say the ROgue had a 30 move speed, that's a total of 120' away. That's far enough to have to find those tracks and then track him (all taking time) while the rogue continues to move forward. Locate Object remains your top option.
How and if you are able to actually track the Rogue may eventually come down to DM storyline. If things don't turn out how you'd like, for any reason, it may be because this is part of the story the DM is telling. Try and do what your characters would do, but also let the DM tell their story - it may turn out to be cooler than catching the thief right away! If the PCs are able to successfully track, the DM may also choose engage the Chase dynamics found in the DMG.